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Tuesday, October 5, 2010
3rd Junior Balkan Mathematical Olympiad Problems 1999
1. a, b, c are distinct reals and there are reals x, y such that a3 + ax + y = 0, b3 + bx + y = 0 and c3 + cx + y = 0. Show that a + b + c = 0. 2. Let an = 23n + 36n+2 + 56n+2. Find gcd(a0, a1, a2, ... , a1999).
